Dependencies and data

# dependencies
library(tidyverse)
library(knitr)
library(kableExtra)
library(boot)
library(parallel)
library(bayestestR)
library(patchwork)
library(mdthemes)
library(lme4)
library(sjPlot)
library(emmeans)
library(ggstance)
library(janitor)
# library(merTools) called via merTools:: to avoid namespace collisions between MASS and dplyr


# set seed for reproducibility
set.seed(42)

# options
options(knitr.table.format = "html") # necessary configuration of tables

# disable scientific notation
options(scipen = 999) 

# function to round all numeric vars in a data frame
round_df <- function(df, n_digits = 3) {
  require(janitor)
  df %>% mutate_if(is.numeric, janitor::round_half_up, digits = n_digits)
}

# create necessary directories
dir.create("../data/processed")
dir.create("../data/results")
#dir.create("models")

# get data 
data_trial_level <- read_csv("../data/raw/data_trial_level.csv") %>%
  filter(timepoint == "baseline" & (age >= 18 | is.na(age)))

# outliers
data_outliers <- data_trial_level %>%
  distinct(unique_id, .keep_all = TRUE) %>%
  select(unique_id, domain, mean_rt) %>%
  mutate(median_mean_rt = median(mean_rt, na.rm = TRUE),
         mad_mean_rt = mad(mean_rt, na.rm = TRUE)) %>%
  # exclude median +- 2MAD
  mutate(rt_outlier = ifelse(mean_rt < median_mean_rt-mad_mean_rt*2 |
                               mean_rt > median_mean_rt+mad_mean_rt*2, TRUE, FALSE)) %>%
  filter(rt_outlier == FALSE) %>%
  select(unique_id, rt_outlier) %>%
  full_join(data_trial_level, by = "unique_id") %>%
  mutate(rt_outlier = ifelse(is.na(rt_outlier), TRUE, rt_outlier))

data_trimmed <- data_outliers %>%
  filter(rt_outlier == FALSE)

# data with confidence intervals
data_estimates_D <- read_csv("../data/processed/data_estimates_D.csv") %>%
  filter(method == "bca")

data_estimates_iat_D <- read_csv("../data/processed/data_estimates_iat_D.csv") %>%
  mutate(trial_type = "iat",
         unique_id = as.factor(unique_id))

CI widths

MAP-MAP width

Most probable estimate among the most probable estimates

data_map_ci_widths <- data_estimates_iat_D %>%
  group_by(domain, trial_type) %>%
  do(point_estimate(.$ci_width, centrality = "MAP")) %>%
  ungroup()

data_map_ci_widths %>%
  summarize(map_map = point_estimate(MAP, centrality = "MAP"),
            min_map = min(MAP),
            max_map = max(MAP)) %>%
  unnest(map_map) %>%
  rename(MAP_MAP = MAP) %>%
  round_df(2) %>%
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)
MAP_MAP min_map max_map
0.71 0.47 0.72

MAP CI width

By domain and trial type using basic bootstrapping, on the basis that it has the best performance for % of non-zero D scores (further below).

data_map_ci_widths %>%
  pivot_wider(names_from = trial_type, values_from = MAP) %>%
  round_df(2) %>%
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)
domain iat
50 Cent - Britney Spears 0.70
African Americans - European Americans 0.70
Artists - Musicians 0.69
Asians - Whites 0.71
Astrology - Science 0.70
Atheism - Religion 0.71
Athletic People - Intelligent People 0.72
Avoiding - Approaching 0.51
Bill Clinton - Hillary Clinton 0.70
Briefs - Boxers 0.69
Burger King - McDonald’s 0.70
Canadian - American 0.71
Capital Punishment - Imprisonment 0.71
Career - Family 0.70
Chaos - Order 0.56
Coffee - Tea 0.70
Cold - Hot 0.71
Conservatives - Liberals 0.68
Corporations - Nonprofits 0.71
David Letterman - Jay Leno 0.71
Denzel Washington - Tom Cruise 0.69
Determinism - Free will 0.67
Difficult - Simple 0.66
Dogs - Cats 0.66
Dramas - Comedies 0.69
Drinking - Abstaining 0.71
Effort - Talent 0.67
Evolution - Creationism 0.70
Fat People - Thin People 0.70
Foreign Places - American Places 0.71
Friends - Family 0.71
Gay People - Straight People 0.71
George Bush - John Kerry 0.71
Gun Control - Gun Rights 0.71
Helpers - Leaders 0.70
Hiphop - Classical 0.71
Innocence - Wisdom 0.70
Japan - United States 0.71
Jazz - Teen Pop 0.70
Jews - Christians 0.71
Jocks - Nerds 0.72
Kobe - Shaq 0.71
Lawyers - Politicians 0.71
Lord of the Rings - Harry Potter 0.70
Manufactured - Natural 0.63
Meat - Vegetables 0.69
Meg Ryan - Julia Roberts 0.70
Microsoft - Apple 0.71
Money - Love 0.47
Mother Teresa - Princess Diana 0.71
Mountains - Ocean 0.71
Muslims - Jews 0.70
National Defense - Education 0.69
New York - California 0.71
Night - Morning 0.68
Numbers - Letters 0.70
Old People - Young People 0.71
Organized Labor - Management 0.71
Pants - Skirts 0.71
Past - Future 0.65
Pepsi - Coke 0.71
Poor People - Rich People 0.56
Private - Public 0.70
Prolife - Prochoice 0.71
Protein - Carbohydrates 0.71
Protestants - Catholics 0.71
Punishment - Forgiveness 0.57
Realism - Idealism 0.71
Reason - Emotions 0.71
Rebellious - Conforming 0.68
Receiving - Giving 0.71
Redsox - Yankees 0.71
Relaxing - Exercising 0.71
Republicans - Democrats 0.68
Rich People - Beautiful People 0.71
Security - Freedom 0.71
Single - Married 0.71
Skeptical - Trusting 0.51
Solitude - Companionship 0.70
Southerners - Northerners 0.70
Speed - Accuracy 0.71
Stable - Flexible 0.71
State - Church 0.71
Strong - Sensitive 0.71
Tall People - Short People 0.70
Tax Reductions - Social Programs 0.71
Team - Individual 0.71
Technology - Nature 0.69
Television - Books 0.70
Tradition - Progress 0.71
Traditional Values - Feminism 0.71
Urban - Rural 0.71
West Coast - East Coast 0.71
Winter - Summer 0.71
Wrinkles - Plastic Surgery 0.71

Plot by domain and trial type

data_ci_width_map_D <- data_estimates_iat_D %>%
  group_by(domain, trial_type) %>%
  do(point_estimate(.$ci_width, centrality = "MAP")) %>%
  ungroup() %>%
  mutate(MAP = round_half_up(MAP, 3),
         trial_type = case_when(trial_type == "tt1" ~ "Trial type 1",
                                trial_type == "tt2" ~ "Trial type 2",
                                trial_type == "tt3" ~ "Trial type 3",
                                trial_type == "tt4" ~ "Trial type 4",
                                trial_type == "iat" ~ "IAT"),
         trial_type = fct_relevel(trial_type, "Trial type 1", "Trial type 2", "Trial type 3", "Trial type 4", "IAT")) %>%
  mutate(domain = fct_rev(domain))

# # save to disk
# write_csv(data_ci_width_map_D, "../data/results/data_ci_width_map_D.csv")

# plot
p_ci_widths <- 
  ggplot(data_ci_width_map_D, aes(MAP, domain)) + 
  geom_point(position = position_dodge(width = 0.8)) +
  mdthemes::md_theme_linedraw() +
  facet_wrap(~ trial_type, ncol = 4, nrow = 1) +
  labs(x = "Highest probability (MAP) 95% CI width",
       y = "") + 
  theme(legend.position = "top")

p_ci_widths

Proportion different from zero

Caterpillar plot

p_cis_by_domain <- 
  data_estimates_iat_D %>%
  arrange(estimate) %>%
  group_by(domain) %>%
  mutate(ordered_id = row_number()/n()) %>%
  ungroup() %>%
  ggplot() +
  geom_linerange(aes(x = ordered_id, ymin = ci_lower, ymax = ci_upper, color = sig),
                 alpha = 1) +
  geom_point(aes(ordered_id, estimate), size = 0.5, shape = "square") +
  geom_hline(yintercept = 0, linetype = "dotted") +
  mdthemes::md_theme_linedraw() +
  theme(axis.text.x = element_blank(),
        axis.ticks.x = element_blank(),
        legend.position = "top") +
  scale_color_viridis_d(end = 0.6, direction = -1) +
  xlab("Ranked participant") +
  ylab("*D* score") +
  labs(color = "95% CI excludes zero point") + 
  facet_wrap(~ domain, ncol = 6)

p_cis_by_domain

Calculate scores

data_diff_zero <- 
  bind_rows(
    mutate(data_estimates_D, measure = "IRAP"),
    mutate(data_estimates_iat_D, measure = "IAT")
  ) %>%
  mutate(measure = fct_relevel(measure, "IRAP", "IAT"),
         domain = as.factor(domain),
         trial_type = case_when(trial_type == "tt1" ~ "Trial type 1",
                                trial_type == "tt2" ~ "Trial type 2",
                                trial_type == "tt3" ~ "Trial type 3",
                                trial_type == "tt4" ~ "Trial type 4",
                                trial_type == "iat" ~ "IAT"),
         trial_type = fct_relevel(trial_type, "Trial type 1", "Trial type 2", "Trial type 3", "Trial type 4", "IAT")) %>%
  group_by(domain, trial_type, measure) %>%
  summarize(proportion_diff_zero = mean(sig),
            variance = plotrix::std.error(sig)^2,
            .groups = "drop") %>%
  # model cannot be run on zero variance or 0 or 1 logit, so offset by a minuscule amount
  mutate(proportion_diff_zero_temp = case_when(proportion_diff_zero < 0.001 ~ 0.001, 
                                               proportion_diff_zero > 0.999 ~ 0.999,
                                               TRUE ~ proportion_diff_zero),
         proportion_diff_zero_logit = boot::logit(proportion_diff_zero_temp)) %>%
  select(-proportion_diff_zero_temp) %>%
  filter(!(proportion_diff_zero == 0 & variance == 0)) %>%
  mutate(variance = ifelse(variance == 0, 0.0001, variance)) 

data_diff_zero
## # A tibble: 227 × 6
##    domain                                trial…¹ measure propo…² varia…³ propo…⁴
##    <fct>                                 <fct>   <fct>     <dbl>   <dbl>   <dbl>
##  1 50 Cent - Britney Spears              IAT     IAT       0.46  2.51e-3 -0.160 
##  2 African Americans - European America… IAT     IAT       0.46  2.51e-3 -0.160 
##  3 Artists - Musicians                   IAT     IAT       0.41  2.44e-3 -0.364 
##  4 Asians - Whites                       IAT     IAT       0.48  2.52e-3 -0.0800
##  5 Astrology - Science                   IAT     IAT       0.5   2.53e-3  0     
##  6 Atheism - Religion                    IAT     IAT       0.58  2.46e-3  0.323 
##  7 Athletic People - Intelligent People  IAT     IAT       0.49  2.52e-3 -0.0400
##  8 Avoiding - Approaching                IAT     IAT       0.95  4.80e-4  2.94  
##  9 Bill Clinton - Hillary Clinton        IAT     IAT       0.43  2.48e-3 -0.282 
## 10 Body image                            Trial … IRAP      0.190 7.71e-3 -1.45  
## # … with 217 more rows, and abbreviated variable names ¹​trial_type,
## #   ²​proportion_diff_zero, ³​variance, ⁴​proportion_diff_zero_logit
## # ℹ Use `print(n = ...)` to see more rows
# # save to disk
# write_csv(data_diff_zero, "../data/results/data_diff_zero.csv")

Plot

p_diff_zero <- 
  data_diff_zero %>%
  filter(measure == "IAT") %>%
  mutate(domain = fct_rev(factor(domain))) %>%
  ggplot(aes(proportion_diff_zero, domain)) +
  geom_linerangeh(aes(xmin = proportion_diff_zero - sqrt(variance)*1.96,
                      xmax = proportion_diff_zero + sqrt(variance)*1.96),
                  position = position_dodge(width = 0.75)) + 
  geom_point(position = position_dodge(width = 0.75)) +
  #scale_shape_manual(labels = c("IRAP", "IAT"), values = c(15, 16)) +
  #scale_color_viridis_d(begin = 0.3, end = 0.7, labels = c("IRAP", "IAT")) +
  mdthemes::md_theme_linedraw() +
  labs(x = "Proportion of scores different from zero point",
       y = "") + 
  theme(legend.position = "top")

p_diff_zero

Model

# fit model
fit_diff_zero <- 
  lmer(proportion_diff_zero_logit ~ 1 + measure + (1 | domain/trial_type),
       weights = 1/variance, 
       data = data_diff_zero,
       # solution from https://www.metafor-project.org/doku.php/tips:rma_vs_lm_lme_lmer
       control = lmerControl(check.nobs.vs.nlev = "ignore",  
                             check.nobs.vs.nRE = "ignore"))

# extract marginal means
results_emm_diff_zero <- 
  summary(emmeans(fit_diff_zero, ~ measure)) %>%
  dplyr::select(measure, estimate = emmean, se = SE, ci_lower = lower.CL, ci_upper = upper.CL)

# extract re Tau
results_re_tau_diff_zero <- fit_diff_zero %>%
  merTools::REsdExtract() %>%
  as_tibble(rownames = "re") %>%
  rename(tau = value) 

# combine
results_diff_zero <- results_emm_diff_zero %>%
  mutate(pi_lower = estimate - (1.96 * sqrt(se^2 + results_re_tau_diff_zero$tau[1]^2)),  # as in metafor package's implementation of prediction intervals, see metafor::predict.rma.R 
         pi_upper = estimate + (1.96 * sqrt(se^2 + results_re_tau_diff_zero$tau[1]^2))) |>
  select(-se) |>
  mutate_if(is.numeric, boot::inv.logit)

# plot
p_prop_nonzero <- 
  ggplot(results_diff_zero, aes(measure, estimate)) +
  geom_linerange(aes(ymin = pi_lower, ymax = pi_upper), size = 0.5, position = position_dodge(width = 0.8), linetype = "dotted") +
  geom_linerange(aes(ymin = ci_lower, ymax = ci_upper), size = 1.25, position = position_dodge(width = 0.8)) +
  geom_point(position = position_dodge(width = 0.8), size = 2.5) +
  mdthemes::md_theme_linedraw() +
  scale_y_continuous(breaks = c(0, .25, .5, .75, 1), labels = c("0.00<br/>(Worse)", "0.25", "0.50", "0.75", "1.00<br/>(Better)")) +
  #scale_color_viridis_d(alpha = 1, begin = 0.3, end = 0.7, labels = c("IRAP", "IAT")) +
  #scale_shape_manual(labels = c("IRAP", "IAT"), values = c(15, 16)) +
  scale_x_discrete(labels = c("IRAP D scores", "IAT D scores")) +
  labs(x = "",
       y = "Proportion of participants with non-zero scores<br/>") + 
  theme(legend.position = "none") +
  coord_flip(ylim = c(0, 1))

p_prop_nonzero

results_diff_zero %>%
  round_df(2) %>%
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)
measure estimate ci_lower ci_upper pi_lower pi_upper
IRAP 0.14 0.12 0.16 0.04 0.39
IAT 0.54 0.51 0.58 0.23 0.83 
# tests
data_emms_diff_zero <- emmeans(fit_diff_zero, list(pairwise ~ measure), adjust = "holm") 

summary(data_emms_diff_zero)$`pairwise differences of measure` %>%
  as.data.frame() %>%
  select(comparison = 1, p.value) %>%
  mutate(p.value = ifelse(p.value < .001, "< .001", round_half_up(p.value, 3))) %>%
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)
comparison p.value
IRAP - IAT < .001

Proportion different from one another

Within domain and trial type.

Note: Discriminability between a score and zero can be determined using the CI, because zero is a known value and only the score is measured with uncertainty. However, discriminability between two scores must take into account the uncertainty in the estimation of both scores. Weir (2005) argues that such an interval can be estimated by expanding the CIs by sqrt(2). Here I refer to these intervals as Discriminability Intervals (DIs).

Calculate discriminability

# helper function to apply workflow to each resample
discriminability <- function(data, i) {
  
  data_with_indexes <- data[i,] # boot function requires data and index
  
  estimate <- data_with_indexes$estimate
  di_lower <- data_with_indexes$di_lower 
  di_upper <- data_with_indexes$di_upper
  
  n_estimate <- length(estimate)
  n_di_lower <- length(di_lower)
  n_di_upper <- length(di_upper)
  
  r_estimate <- sum(rank(c(estimate, di_lower))[1:n_estimate])
  r_di_upper <- sum(rank(c(di_upper, estimate))[1:n_di_upper])
  
  prob_estimate_inferior_to_di_lower <- 1 - (r_estimate / n_estimate - (n_estimate + 1) / 2) / n_di_lower
  prob_estimate_superior_to_di_upper <- 1 - (r_di_upper / n_di_upper - (n_di_upper + 1) / 2) / n_estimate
  
  probability_estimates_outside_cis <- (prob_estimate_inferior_to_di_lower + prob_estimate_superior_to_di_upper)
  
  return(probability_estimates_outside_cis)
  
}

bootstrap_discriminability <- function(data){
  
  require(dplyr)
  require(boot)
  
  fit <- 
    boot::boot(data      = data, 
               statistic = discriminability, 
               R         = 5000,
               sim       = "ordinary", 
               stype     = "i",
               parallel  = "multicore", 
               ncpus     = parallel::detectCores()-1)
  
  results <- boot::boot.ci(fit, conf = 0.95, type = "bca") 
  
  output <-
    tibble(
      estimate = fit$t0,
      ci_lower = results$bca[4],
      ci_upper = results$bca[5]
    )
  
  return(output)
}

# irap data
data_discriminability_D <- read_csv("../data/results/data_discriminability_D.csv") %>%
    filter(method == "bca")

# bootstrapping has a long execution time, so load saved values if they've already been calculated
if(file.exists("../data/results/data_discriminability_iat_D.csv")) {
  
  data_discriminability_iat_D <- read_csv("../data/results/data_discriminability_iat_D.csv")
  
} else {
  
  # bootstrap D scores 
  data_discriminability_iat_D <- data_estimates_iat_D |>
    # expand CIs by sqrt(2) to form discriminability intervals
    mutate(di_lower = estimate - (estimate - ci_lower)*sqrt(2),
           di_upper = estimate + (ci_upper - estimate)*sqrt(2)) |>
    select(unique_id, domain, trial_type, estimate, di_upper, di_lower) |>
    group_by(domain, trial_type) |>
    do(bootstrap_discriminability(data = .)) |>
    ungroup() |>
    rename(proportion_discriminable = estimate) |>
    mutate(variance = ((ci_upper - ci_lower)/(1.96*2))^2,
           domain = as.factor(domain),
           trial_type = fct_relevel(trial_type, "tt1", "tt2", "tt3", "tt4", "iat"),
           measure = "IAT") 
  
  # save to disk
  write_csv(data_discriminability_iat_D, "../data/results/data_discriminability_iat_D.csv")
  
}

Plot

# combine
data_discriminability_combined <- 
  bind_rows(
    mutate(data_discriminability_D, measure = "IRAP"),
    mutate(data_discriminability_iat_D, measure = "IAT")
  ) %>%
  mutate(measure = fct_relevel(measure, "IRAP", "IAT"),
         trial_type = case_when(trial_type == "tt1" ~ "Trial type 1",
                                trial_type == "tt2" ~ "Trial type 2",   
                                trial_type == "tt3" ~ "Trial type 3",   
                                trial_type == "tt4" ~ "Trial type 4",
                                trial_type == "iat" ~ "IAT"),
         trial_type = fct_relevel(trial_type, "Trial type 1", "Trial type 2", "Trial type 3", "Trial type 4", "IAT")) %>%
  filter(!(proportion_discriminable == 0 & variance == 0)) %>%
  mutate(variance = ifelse(variance == 0, 0.0001, variance)) |>
  # model cannot be run on zero variance or 0 or 1 logit, so offset by a minuscule amount
  mutate(
    proportion_discriminable_temp = case_when(proportion_discriminable < 0.001 ~ 0.001, 
                                              proportion_discriminable > 0.999 ~ 0.999,
                                              TRUE ~ proportion_discriminable),
    proportion_discriminable_logit = boot::logit(proportion_discriminable_temp)
  ) %>%
  select(-proportion_discriminable_temp)

p_discriminability <- 
  data_discriminability_combined %>%
  filter(measure == "IAT") %>%
  mutate(domain = fct_rev(factor(domain))) %>%
  ggplot(aes(proportion_discriminable, domain)) +
  geom_linerangeh(aes(xmin = proportion_discriminable - sqrt(variance)*1.96,
                      xmax = proportion_discriminable + sqrt(variance)*1.96),
                  position = position_dodge(width = 0.75)) + 
  geom_point(position = position_dodge(width = 0.75)) +
  #scale_shape_manual(labels = c("IRAP", "IAT"), values = c(15, 16)) +
  #scale_color_viridis_d(begin = 0.3, end = 0.7, labels = c("IRAP", "IAT")) +
  mdthemes::md_theme_linedraw() +
  facet_wrap(~ trial_type, ncol = 4) +
  labs(x =  "Proportion of participants<br/>whose scores differ from one another<br/>",
       y = "",
       color = "Scoring method",
       shape = "Scoring method") + 
  theme(legend.position = "top")

p_discriminability

Model

# fit meta analytic model
fit_disciminability <- 
  lmer(proportion_discriminable_logit ~ 1 + measure + (1 | domain/trial_type), 
       weights = 1/variance, 
       data = data_discriminability_combined,
       # solution from https://www.metafor-project.org/doku.php/tips:rma_vs_lm_lme_lmer
       control = lmerControl(check.nobs.vs.nlev = "ignore",  
                             check.nobs.vs.nRE = "ignore"))

# extract marginal means
results_emm_disciminability <-
  summary(emmeans(fit_disciminability, ~ measure)) %>%
  dplyr::select(measure, estimate = emmean, se = SE, ci_lower = lower.CL, ci_upper = upper.CL) 

# extract re Tau
results_re_tau_disciminability <- fit_disciminability %>%
  merTools::REsdExtract() %>%
  as_tibble(rownames = "re") %>%
  rename(tau = value) 

# combine
results_disciminability <- results_emm_disciminability %>%
  mutate(pi_lower = estimate - (1.96 * sqrt(se^2 + results_re_tau_disciminability$tau[1]^2)),  # as in metafor package's implementation of credibility intervals, see metafor::predict.rma.R
         pi_upper = estimate + (1.96 * sqrt(se^2 + results_re_tau_disciminability$tau[1]^2))) |>
  select(-se) |>
  mutate_if(is.numeric, boot::inv.logit)

# plot
p_prop_discriminable <-
  ggplot(results_disciminability, aes(measure, estimate)) +
  geom_linerange(aes(ymin = pi_lower, ymax = pi_upper), size = 0.5, position = position_dodge(width = 0.8), linetype = "dotted") +
  geom_linerange(aes(ymin = ci_lower, ymax = ci_upper), size = 1.25, position = position_dodge(width = 0.8)) +
  geom_point(position = position_dodge(width = 0.8), size = 2.5) +
  scale_y_continuous(breaks = c(0, .25, .5, .75, 1), labels = c("0.00<br/>(Worse)", "0.25", "0.50", "0.75", "1.00<br/>(Better)")) +
  #scale_shape_manual(labels = c("IRAP", "IAT"), values = c(15, 16)) +
  #scale_color_viridis_d(begin = 0.3, end = 0.7, labels = c("IRAP", "IAT")) +
  scale_x_discrete(labels = c("IRAP D scores", "IAT D scores")) +
  mdthemes::md_theme_linedraw() +
  labs(x = "",
       y = "Proportion of participants<br/>whose scores differ from one another<br/>") +
  theme(legend.position = "none") +
  coord_flip(ylim = c(0, 1))

p_prop_discriminable 

results_disciminability %>%
  round_df(2) %>%
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)
measure estimate ci_lower ci_upper pi_lower pi_upper
IRAP 0.07 0.06 0.08 0.03 0.17
IAT 0.43 0.40 0.46 0.21 0.67 
# tests
data_emms_disciminability <- emmeans(fit_disciminability, list(pairwise ~ measure), adjust = "holm")

summary(data_emms_disciminability)$`pairwise differences of measure` %>%
  as.data.frame() %>%
  select(comparison = 1, p.value) %>%
  mutate(p.value = ifelse(p.value < .001, "< .001", round_half_up(p.value, 3))) %>%
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)
comparison p.value
IRAP - IAT < .001

CI widths as a proportion of observed range

NB observed range of confidence intervals

Calculate scores

## calculate observed ranges 
observed_range_estimates_D <- data_estimates_D %>%
  group_by(domain, trial_type) %>%
  dplyr::summarize(min = min(ci_lower, na.rm = TRUE),
                   max = max(ci_upper, na.rm = TRUE),
                   .groups = "drop") %>%
  mutate(range = max - min) 

observed_range_estimates_iat_D <- data_estimates_iat_D %>%
  group_by(domain) %>%
  dplyr::summarize(min = min(ci_lower, na.rm = TRUE),
                   max = max(ci_upper, na.rm = TRUE),
                   .groups = "drop") %>%
  mutate(range = max - min) 

# calculate CI / range 
data_ci_width_proportions_D <- data_estimates_D %>%
  # join this data into the original data
  full_join(observed_range_estimates_D, by = c("domain", "trial_type")) %>%
  # calculate ci width as a proportion of observed range
  mutate(ci_width_proportion = ci_width / range) %>%
  mutate(measure = "IRAP") 

data_ci_width_proportions_iat_D <- data_estimates_iat_D %>%
  # join this data into the original data
  full_join(observed_range_estimates_iat_D, by = "domain") %>%
  # calculate ci width as a proportion of observed range
  mutate(ci_width_proportion = ci_width / range) %>%
  mutate(measure = "IAT")

# combine
data_ci_width_proportions_combined <- 
  bind_rows(
    data_ci_width_proportions_D,
    data_ci_width_proportions_iat_D
  ) %>%
  mutate(measure = fct_relevel(measure, "IRAP", "IAT"),
         domain = as.factor(domain),
         trial_type = fct_relevel(trial_type, "tt1", "tt2", "tt3", "tt4", "iat")) %>%
  # logit transform
  mutate(ci_width_proportion_temp = case_when(ci_width_proportion < 0.0001 ~ 0.0001,
                                              ci_width_proportion > 0.9999 ~ 0.9999,
                                              TRUE ~ ci_width_proportion),
         ci_width_proportion_logit = boot::logit(ci_width_proportion_temp)) %>%
  select(-ci_width_proportion_temp)

Model

# fit model
fit_ci_width_proportions <- 
  lmer(ci_width_proportion_logit ~ 1 + measure + (1 | domain/trial_type), 
       data = data_ci_width_proportions_combined,
       # solution from https://www.metafor-project.org/doku.php/tips:rma_vs_lm_lme_lmer
       control = lmerControl(check.nobs.vs.nlev = "ignore",  
                             check.nobs.vs.nRE = "ignore"))

# extract marginal means
results_emm_ci_width_proportions <-
  summary(emmeans(fit_ci_width_proportions, ~ measure)) %>%
  dplyr::select(measure, estimate = emmean, se = SE, ci_lower = asymp.LCL, ci_upper = asymp.UCL)

# extract re Tau
results_re_tau_ci_width_proportions <-
  merTools::REsdExtract(fit_ci_width_proportions) %>%
  as_tibble(rownames = "re") %>%
  rename(tau = value)

# combine
results_ci_width_proportions <- results_emm_ci_width_proportions %>%
  mutate(pi_lower = estimate - (1.96 * sqrt(se^2 + results_re_tau_ci_width_proportions$tau[1]^2)),  # as in metafor package's implementation of credibility intervals, see metafor::predict.rma.R
         pi_upper = estimate + (1.96 * sqrt(se^2 + results_re_tau_ci_width_proportions$tau[1]^2))) %>%
  select(-se) %>%
  mutate_if(is.numeric, boot::inv.logit)

# plot
p_ci_width_proportion_observed_range <-
  ggplot(results_ci_width_proportions, aes(measure, estimate, 
  )) +
  geom_linerange(aes(ymin = pi_lower, ymax = pi_upper), size = 0.5, position = position_dodge(width = 0.8), linetype = "dotted") +
  geom_linerange(aes(ymin = ci_lower, ymax = ci_upper), size = 1.25, position = position_dodge(width = 0.8)) +
  geom_point(position = position_dodge(width = 0.8), size = 2.5) +
  #scale_shape_discrete(labels = c("IRAP", "IAT")) +
  scale_y_continuous(breaks = c(0, .25, .5, .75, 1), labels = c("0.00<br/>(Better)", "0.25", "0.50", "0.75", "1.00<br/>(Worse)")) +
  #scale_shape_manual(labels = c("IRAP", "IAT"), values = c(15, 16)) +
  #scale_color_viridis_d(begin = 0.3, end = 0.7, labels = c("IRAP", "IAT")) +
  scale_x_discrete(labels = c("IRAP D scores", "IAT D scores")) +
  mdthemes::md_theme_linedraw() +
  labs(x = "",
       y = "Proportion of observed range covered<br/>by individual participants' 95% CIs") +
  theme(legend.position = "none") +
  coord_flip(ylim = c(0, 1))

p_ci_width_proportion_observed_range

results_ci_width_proportions %>%
  round_df(2) %>%
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)
measure estimate ci_lower ci_upper pi_lower pi_upper
IRAP 0.52 0.50 0.53 0.43 0.60
IAT 0.26 0.26 0.27 0.21 0.33 
# tests
data_emms_ci_width_proportions <- emmeans(fit_ci_width_proportions, list(pairwise ~ measure), adjust = "holm") 

summary(data_emms_ci_width_proportions)$`pairwise differences of measure` %>%
  as.data.frame() %>%
  select(comparison = 1, p.value) %>%
  mutate(p.value = ifelse(p.value < .001, "< .001", round_half_up(p.value, 3))) %>%
  kable() %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = FALSE)
comparison p.value
IRAP - IAT < .001

Combined plots

Plot 4

p_cis_by_domain

ggsave(filename  = "plots/figure_4_cis_by_domain_irap_vs_iat.pdf",
       plot      = p_cis_by_domain,
       device    = "pdf",
       # path      = NULL,
       # dpi       = 300,
       units     = "in",
       width     = 8,
       height    = 16,
       limitsize = TRUE)

Plot 5

p_ci_widths

ggsave(filename  = "plots/figure_5_ci_widths_irap_vs_iat.pdf",
       plot      = p_ci_widths,
       device    = "pdf",
       # path      = NULL,
       # dpi       = 300,
       units     = "in",
       width     = 6,
       height    = 12,
       limitsize = TRUE)

Plot 6

p_combined <- 
  p_prop_nonzero + 
  p_prop_discriminable + 
  p_ci_width_proportion_observed_range +
  plot_layout(ncol = 1) #, guides = "collect") & theme(legend.position = "top")

p_combined

ggsave(filename  = "plots/figure_6_metaanalyses_irap_vs_iat.pdf",
       plot      = p_combined,
       device    = "pdf",
       # path      = NULL,
       # dpi       = 300,
       units     = "in",
       width     = 5,
       height    = 5,
       limitsize = TRUE)

Session info

sessionInfo()
## R version 4.2.0 (2022-04-22)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Big Sur/Monterey 10.16
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.2/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_IE.UTF-8/en_IE.UTF-8/en_IE.UTF-8/C/en_IE.UTF-8/en_IE.UTF-8
## 
## attached base packages:
## [1] parallel  stats     graphics  grDevices utils     datasets  methods  
## [8] base     
## 
## other attached packages:
##  [1] janitor_2.1.0     ggstance_0.3.5    emmeans_1.7.3     sjPlot_2.8.10    
##  [5] lme4_1.1-29       Matrix_1.4-1      mdthemes_0.1.0    patchwork_1.1.1  
##  [9] bayestestR_0.12.1 boot_1.3-28       kableExtra_1.3.4  knitr_1.39       
## [13] forcats_0.5.1     stringr_1.4.0     dplyr_1.0.9       purrr_0.3.4      
## [17] readr_2.1.2       tidyr_1.2.0       tibble_3.1.8      ggplot2_3.3.6    
## [21] tidyverse_1.3.1  
## 
## loaded via a namespace (and not attached):
##   [1] TH.data_1.1-1       minqa_1.2.4         colorspace_2.0-3   
##   [4] ellipsis_0.3.2      sjlabelled_1.2.0    estimability_1.3   
##   [7] snakecase_0.11.0    markdown_1.1        parameters_0.18.1  
##  [10] fs_1.5.2            gridtext_0.1.4      ggtext_0.1.1       
##  [13] rstudioapi_0.13     listenv_0.8.0       furrr_0.3.0        
##  [16] farver_2.1.1        bit64_4.0.5         fansi_1.0.3        
##  [19] mvtnorm_1.1-3       lubridate_1.8.0     xml2_1.3.3         
##  [22] codetools_0.2-18    splines_4.2.0       sjmisc_2.8.9       
##  [25] jsonlite_1.8.0      nloptr_2.0.3        ggeffects_1.1.2    
##  [28] pbkrtest_0.5.1      broom_0.8.0         dbplyr_2.1.1       
##  [31] broom.mixed_0.2.9.4 shiny_1.7.1         effectsize_0.6.0.1 
##  [34] compiler_4.2.0      httr_1.4.3          sjstats_0.18.1     
##  [37] backports_1.4.1     assertthat_0.2.1    fastmap_1.1.0      
##  [40] cli_3.3.0           later_1.3.0         htmltools_0.5.2    
##  [43] tools_4.2.0         coda_0.19-4         gtable_0.3.0       
##  [46] glue_1.6.2          merTools_0.5.2      Rcpp_1.0.9         
##  [49] cellranger_1.1.0    jquerylib_0.1.4     vctrs_0.4.1        
##  [52] svglite_2.1.0       nlme_3.1-157        iterators_1.0.14   
##  [55] insight_0.18.0      xfun_0.31           globals_0.14.0     
##  [58] rvest_1.0.2         mime_0.12           lifecycle_1.0.1    
##  [61] future_1.25.0       MASS_7.3-56         zoo_1.8-10         
##  [64] scales_1.2.0        vroom_1.5.7         promises_1.2.0.1   
##  [67] hms_1.1.1           sandwich_3.0-1      yaml_2.3.5         
##  [70] sass_0.4.1          stringi_1.7.8       highr_0.9          
##  [73] foreach_1.5.2       plotrix_3.8-2       blme_1.0-5         
##  [76] rlang_1.0.4         pkgconfig_2.0.3     systemfonts_1.0.4  
##  [79] arm_1.12-2          evaluate_0.15       lattice_0.20-45    
##  [82] labeling_0.4.2      bit_4.0.4           tidyselect_1.1.2   
##  [85] parallelly_1.31.1   magrittr_2.0.3      R6_2.5.1           
##  [88] generics_0.1.2      multcomp_1.4-19     DBI_1.1.2          
##  [91] pillar_1.8.0        haven_2.5.0         withr_2.5.0        
##  [94] abind_1.4-5         survival_3.3-1      datawizard_0.4.1   
##  [97] performance_0.9.1   modelr_0.1.8        crayon_1.5.1       
## [100] utf8_1.2.2          tzdb_0.3.0          rmarkdown_2.14     
## [103] grid_4.2.0          readxl_1.4.0        reprex_2.0.1       
## [106] digest_0.6.29       webshot_0.5.3       xtable_1.8-4       
## [109] httpuv_1.6.5        munsell_0.5.0       viridisLite_0.4.0  
## [112] bslib_0.3.1